POPULATION PHARMACOKINETICS
POPULATION PHARMACOKINETICS
RAYMOND MILLER, D.Sc.Pfizer Global Research and Development
RAYMOND MILLER, D.Sc.Pfizer Global Research and Development
Population Pharmacokinetics
Definition
Advantages/Disadvantages
Objectives of Population Analyses
Impact in Drug Development
Population pharmacokinetics describe
The typical relationships between physiology (both normal and disease altered) and pharmacokinetics/pharmacodynamics,
The interindividual variability in these relationships, and
Their residual intraindividual variability.
Sheiner-LBDrug-Metab-Rev. 1984; 15(1-2): 153-71
Definition
Definition
E.g.: A simple Pk model
Ri = infusion rate
Cl = drug clearance
k =elimination rate constant
= measurement error, intra-individual error
Dru
g C
onc
Time N(0,)
kteCl
RiCp 1
DefinitionD
rug
Con
c
Time
ss
ktss
kt
Cp
RiCl
eCpCp
eCl
RiCp
1
1
Cl = metabolic clearance + renal clearance
Cl = 1 + 2• CCr
Dru
g C
lea
ran
ce
Creatinine Clearance
Dru
g C
onc
Time
Definition
Cl = metabolic clearance + renal clearance
Cl = 1 + 2• CCr
Dru
g C
lea
ran
ce
Creatinine Clearance
N(0,)
Definition
Graphical illustration of the statistical model used in NONMEM for the special case of a one compartment model with first order absorption. (Vozeh et al. Eur J Clin Pharmacol 1982;23:445-451)
crkk ClCl 222211
Objectives
1. Provide Estimates of Population PK Parameters (CL, V) - Fixed Effects
2. Provide Estimates of Variability - Random Effects
• Intersubject Variability• Interoccasion Variability (Day to Day Variability)• Residual Variability (Intrasubject Variability,
Measurement Error, Model Misspecification)
Objectives
3. Identify Factors that are Important Determinants of Intersubject Variability
• Demographic: Age, Body Weight or Surface Area, gender, race
• Genetic: CYP2D6, CYP2C19• Environmental: Smoking, Diet• Physiological/Pathophysiological: Renal (Creatinine
Clearance) or Hepatic impairment, Disease State • Concomitant Drugs• Other Factors: Meals, Circadian Variation,
Formulations
Advantages
•Sparse Sampling Strategy (2-3 concentrations/subject)–Routine Sampling in Phase II/III Studies–Special Populations (Pediatrics, Elderly)
•Large Number of Patients –Fewer restrictions on inclusion/exclusion criteria
•Unbalanced Design–Different number of samples/subject
•Target Patient Population–Representative of the Population to be Treated
Disadvantages
•Quality Control of Data–Dose and Sample Times/Sample Handling/
Inexperienced Clinical Staff
•Timing of Analytical Results/Data Analyses
•Complex Methodology –Optimal Study Design (Simulations) –Data Analysis
•Resource Allocation•Unclear Cost/Benefit Ratio
Dru
g C
onc
Time
Models are critical in sparse sampling situations:
Dru
g C
onc
Time
Models are critical in sparse sampling situations:
Dru
g C
onc
Time
Models are critical in sparse sampling situations:
Dru
g C
onc
Time
Models are critical in sparse sampling situations:
Dru
g C
onc
Time
Models are critical in sparse sampling situations:
Dru
g C
onc
Time
Models are critical in sparse sampling situations:
Study Objectives
To evaluate the efficacy of drug treatment or placebo as add on treatment in patients with partial seizures.
Data Structure
Study N Doses Explored
1 308 0, 600 mg/day (bid & tid)
2 287 0, 150, 600 mg/day (tid)
3 447 0,50,150,300,600 mg/day (bid)
Total 1092
Baseline Placebo
Count Model
!)(
xexYP
x
i
represents the expected number of events per unit time
E(Yij)=itij
The natural estimator of is the overall observed rate for the group.
timeTotal
countsTotal
!)(
xexYP
x
i
Suppose there are typically 5 occurrences per month in a group of patients:- =5
!)(
xexYP
x
i
The mean number of seizure episodes per month (λ) was modeled using NONMEM as a function of drug dose, placebo, baseline and subject specific random effects.
drugplaceboBaseline
Baseline = estimated number of seizures reported during baseline period
Placebo = function describing placebo response
Drug = function describing the drug effect
= random effect
Sub-population analysis
Some patients are refractory to any particular drug at any dose.
Interest is in dose-response in patients that respond
Useful in adjusting dose in patients who would benefit from treatment
Investigate the possibility of at least two sub-populations.
11111 drugplaceboBaseline
22222 drugplaceboBaseline
Population A (p)
Population B (1-p)
Mixture Model
A model that implicitly assumes that some fraction p of the population has one set of typical values of response, and that the remaining fraction 1-p has another set of typical values
101 11.0
186
111.11
%75
eDDDose
Dose
APopulation
Final Model
201 44.126.011.15
%25 eDD
BPopulation
Expected percent reduction inseizure frequency
Monte Carlo simulation using parameters and variance for Subgroup A
8852 individuals (51% female)
% reduction from baseline seizure frequency calculated
Percentiles calculated for % reduction in seizure frequency at each dose
Results
Estimated population parameters for the exposure-response relationship of seizure frequency to pregabalin or gabapentin dose. Parameter Parameter Estimates (95% CI) Gabapentin Pregabalin BaseA (seizures/month) 14.0 (12.4,15.6) 11.1 (10.2,12.0) BaseB (seizures/month) 16.8 (8.8,24.8) 15.1 (12.3,17.9) EmaxA (maximal fractional change) -0.25 (-0.31,-0.18) -1.0 EmaxB (maximal fractional change) 2.34 (0.20,4.48) 0.26(-0.15,0.66) PlaceboA (maximal fractional change) -0.15 (-0.29,-0.009) -0.11 (-0.18,-0.03) PlaceboB (maximal fractional change) 4.34 (-0.80,9.47) 1.44 (0.66,2.22) ED50 (mg) 463.0 (161.3,764.7) 186.0 (91.4,280.6) ProportionA 0.95 (0.93,0.98) 0.75(0.61,0.88)
Conclusions
A comparison of the dose-response relationship for gabapentin and pregabalin reveals that pregabalin was 2.5 times more potent, as measured by the dose that reduced seizure frequency by 50% (ED50).
Pregabalin was more effective than gabapentin based on the magnitude of the reduction in seizure frequency (Emax)
Three hundred clinical trials for each drug were simulated conditioned on the original study designs. Each simulated trial was analyzed to estimate % median change in seizure frequency. The observed and model-predicted treatment effects of median reduction in seizure frequency for gabapentin and pregabalin are illustrated for all subjects and for responders. Data points represent median percentage change from baseline in seizure frequency for each treatment group (including placebo). The shaded area corresponds to predicted 10th and 90th percentiles for median change from baseline in seizure frequency.
Relationship Between %Change in Seizure Frequency (Relative to Baseline) and Daily Dosage of Gabapentin and Pregabalin
• Dose-response model in epilepsy using pooled analysis of 4 gabapentin studies + 3 pregabalin studies
Dose (mg/Day)
Me
dia
n %
Ch
an
ge
in
Se
izu
re F
req
ue
ncy
fro
m B
ase
line
0 300 600 900 1200 1500 1800
-60
-40
-20
02
0
GabapentinPregabalin
Relationship Between %Change in Seizure Frequency (Relative to Baseline) and Daily Dosage of Gabapentin and Pregabalin in Responders to Treatment
Dose (mg/Day)
Med
ian
% C
hang
e in
Sei
zure
Fre
quen
cy f
rom
Bas
elin
e
0 300 600 900 1200 1500 1800
-80
-60
-40
-20
02
04
0
GabapentinPregabalin
Dose-response model in epilepsy using pooled analysis of 4 gabapentin studies + 3 pregabalin studies
Clinical Trial Simulation
Used to assess how different design and drug factors may affect trial performance.
May be viewed as an extension of statistical design evaluation.
Planning Phase 2 POC for Alzheimer's Disease Drug
Because the mechanism of action of CI-1017 was untested clinically, the principle objective of the clinical study was to ascertain whether CI-1017 improved cognitive performance at least as fast and as well as tacrine.
This would be considered proof of concept (POC).
Typical Effectiveness Trials (AD)
Parallel group design
Two to four treatment groups + placebo
Powered to detect 3 point improvement in ADAS-Cog
Minimum 12 weeks of treatment
• Require about 80 subjects per dose group to have 90% power (2 sided 50% sig. Level)
Simulation Model
DRUGPLACEBONPROGRESSIODISEASEBASELINECogADAS
30%IIV Random
curvesresponsedoseltheoretica4
DRUG
eePLACEBO
timeNPROGRESSIODISEASE
BASELINE
Where:
ttScale
rate
base
onoff
Drug effect models considered in simulations study. Parameters characterizing the model are displayed in the individual panels (Lockwood et al.)
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90
CI-1017 average steady state plasma concentration (ng/mL)
-4
-3
-2
-1
0
chan
ge in
AD
AS
-cog
sco
re
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36CI-1017 tid dose (mg)
Effect size at 25mg = -3
Effect/dose slope = - 0.12
Effect/conc slope = - 0.047
linear dose response model
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90
CI-1017 average steady state plasma concentration (ng/mL)
-4
-3
-2
-1
0
chan
ge in
AD
AS
-cog
sco
re
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36CI-1017 tid dose (mg)
Effect size at 25 mg tid = -3 = 75% Emax
ED50 ~ 8.5 mg
EC50 ~ 21 ng/mL
1/2 maximal effect = -2
Hyperbolic (Emax) dose response model
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90
CI-1017 average steady state plasma concentration (ng/mL)
-4
-3
-2
-1
0
chan
ge in
AD
AS
-cog
sco
re
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36CI-1017 tid dose (mg)
Effect size at 25 mg = 100% Emax = -3
ED50 ~ 8 mg
EC50 ~ 21 ng/mL
Hill coefficient = 4
Sigmoidal (Smax) dose response model
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90
CI-1017 averge steady state plasma concentration (ng/mL)
-6
-5
-4
-3
-2
-1
00 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
CI-1017 tid dose (mg)
Combined agonist-antagonist dose/responseAgonist (Emax) dose/responseAntagonist (Imax) dose/response
chan
ge in
AD
AS
-cog
sco
re
Overall effect size at 10mg tid = -3
ED50 Imax ~ 15 mg
U shaped dose response model
ED50 Emax ~ 7 mg
TRIAL DESIGN
Design number
Design description Number of sequences
Subjects per sequence
Number of treatments
periods
Period length (weeks) Measurements per period
1 6X6 Latin Square 6 10 6 2 1
2 6X3 Incomplete block 6 10 3 4 2
3 Parallel group 6 10 1 12 6
4 6X4 Incomplete block 6 10 4 3 1
5 6X3 Incomplete block with 2 parallel groups
8 8 Seq 1-6: 3Seq 7-8: 1
Seq 1-6: 4Seq 7-8:12
26
6 4X4 Latin Square 4 15 4 3 1
7 4X4 Latin Square with 2 parallel groups
6 10 Seq 1-4: 4Seq 5-6: 1
312
16
8 4X4 Latin Square 4 15 4 4 2
DATA EVALUATION
DOES THE DRUG WORK?• AOV to test null hypothesis of no drug effect• Rejection of null hypothesis judged correct• Dose trend test
IS THE SHAPE MONOTONIC OR U-SHAPED?• Similar to the above two steps• Non-positive trial pattern classified as flat• Inference between monotonic and u-shaped based on
highest dose having best mean outcome.
SIMULATION
100 Trial simulations
Pharsight trial simulator (TS2)
Data from each trial analyzed
Conclusions scored
DRUG EFFECT
Design number 8 7 6
Dose response shape
Linear 84 41 51
Emax 88 58 67
Smax 96 75 85
U-shape 57 40 49
AVERAGE 81 54 63
Design number 6: 4X4 Latin Square, 3 weeks per treatment.Design number 7: 4X4 Latin Square with 2 parallel groups,Design number 8, 4X4 Latin Square, 4 weeks per treatment
Percent of 100 trials (power) that detected a drug effect for design number 6, 7 and 8.
SHAPE
Percent of 100 trials (power) that correctly identified dose-response shape for design number 6, 7 and 8
Design number 8 7 6
Dose response shape
Linear 96 69 72
Emax 84 62 74
Smax 96 83 89
U-shape 45 34 39
AVERAGE 80 62 69
Simulation ConclusionsDesign
4x4 LS with 4-week periods using bi-weekly measurements • Was best among alternatives considered for
detecting activity and identifying DR shape• Met minimum design criteria (80% average power)
Results
4x4 LS design was accepted, conducted, and analyzed more-or-less as recommended
Unfortunately, drug didn’t work• But we were able to find this out more quickly and
with less resources than with conventional design
Gabapentin – Neuropathic PainNDA
Two adequate and well controlled clinical trials submitted.
Indication – post-herpetic neuralgia
Trials used different dose levels• 1800 mg/day and 2400 mg/day• 3600 mg/day
The clinical trial data was not replicated for each of the dose levels sought in the drug application
FDAMA 1997
FDA review staff decided to explore whether PK/PD analyses could provide the confirmatory evidence of efficacy.
“—based on relevant science, that data from one adequate and well controlled clinical investigation and confirmatory evidence (obtained prior to or after such investigation) are sufficient to establish effectiveness.”
SIMULATION
100 Trial simulations
Pharsight trial simulator (TS2)
Data from each trial analyzed
Conclusions scored
Gabapentin Study Designs for PHN
Used all daily pain scores (27,678 observations)
Exposure-response analysis included titration data for within-subject dose response
Table 1. Overview of PHN Controlled Studies: Double-Blind Randomized/Target Dose and ITT Population Duration of Double-Blind Phase Number of Patients
Final Gabapentin Dose, mg/day
Study Titration Fixed Dose
Overall Duration Placebo 600 1200 1800 2400 3600
Any Gabapentin
All Patients
945-211 4 Weeks 4 Weeks 8 Weeks 116 -- -- -- -- 113 113 229 945-295 (-430) 3 Weeks 4 Weeks 7 Weeks 111 -- -- 115 108 -- 223 334 945-306 4 Weeks 4 Weeks 8 Weeks 152 -- -- -- 153 -- 153 305 Total Patients 379 0 0 115 261 113 489 868 -- Dose group not included in study design ITT Population = All randomized patients who received at least one dose of study medication.
Gabapentin Response in PHN
Time Dependent Placebo Response, Emax Drug Response and Saturable Absorption,
945-295
Time (Days)
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46
Mea
n P
ain
Sco
re
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0 Placebo (Observed)1800 mg Daily (Observed)2400 mg Daily (Observed)Placebo (Predicted)1800 mg Daily (Predicted)2400 mg Daily (Predicted)
945-295
Time (Days)
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46
Mea
n P
ain
Sco
re
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0 Placebo (Observed)1800 mg Daily (Observed)2400 mg Daily (Observed)Placebo (Predicted)1800 mg Daily (Predicted)2400 mg Daily (Predicted)
945-211
Time (Days)
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Mea
n P
ain
Sco
re
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Placebo (Observed)Placebo (Predicted)3600 mg Daily (Observed)3600 mg Daily (Predicted)
945-211
Time (Days)
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Mea
n P
ain
Sco
re
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Placebo (Observed)Placebo (Predicted)3600 mg Daily (Observed)3600 mg Daily (Predicted)
Results
Summary statistics showed pain relief for both studies at different doses concur.
M & S showed pain scores for both studies can be predicted with confidence from the comparative pivotal study (cross confirming).
Conclusion The use of PK/PD modeling and simulation
confirmed efficacy across the three studied doses, obviating the need for additional clinical trials.
Gabapentin was subsequently approved by FDA for post-herpetic neuralgia
The package insert states “pharmacokinetic/pharmacodynamic modeling provided confirmatory evidence of efficacy across all doses”